I'm an Econ grad student currently not paying attention in a Maths class (something about the Implicit Function Theorem) and I'm absolutely intrigued by your two comments. Kudos.
Also, to sidetrack a little bit, may I ask how long it took you to gather these thoughts and post them? I'm trying to get a sense of how far along I am about gaining a holistic understanding of markets and trading.
While I don't think any time taken is necessarily a great indicator of general understanding, I was struck by a great feeling of unease while reading 1e-9's comment. Initially I sought to understand the apparent contradiction in the measurable reduction in arbitrage opportunity as a generally accepted proxy measure for increasing market efficiencies with my general understanding that HFT generally massively increases volatility and does not generally appear to result in the reduction of instrument pricing due to lower trading overheads and losses. I also sought to explain the seemingly unending profit stream made possible by such strategies - when, paradoxically the more efficient the market becomes, the less profitable all HFT stratigies should become globally - and yet, it does not seem they do.
All in all, about 10 minutes or so of consideration, followed by about an half an hour of editing.
That said, I'll likely spend much more time looking for existing models of financial markets under the information relativistic conditions created by HFT activity - it occurs to me that as trading moves closer to speed of causality in the market the models underlying market understanding may need to be adapted, perhaps using relativity as a prototype. With any luck they already have and I can elaborate from those to solve for conditions of such markets with information asymmetry and agents capturing value. If such markets are inherently volatile and that volatility increases geometrically nearing the speed of causality - presumably, the speed of light, then this may provide the mechanism for the apparent global inflation of instrument prices via distributed profitable high-speed trading activity while preserving lessened arbitrage opportunity and other visible market behaviours.
I really must formalise this so that it may be thoroughly and logically evaluated - both symbolically and under simulation. However, I'm at a disadvantage in that I am merely a dabbler in the field of economics and game theory. I also have no formal background in stochastic finance or physics. I am but a Systems Engineer. So, fun challenges ahead.
Of course, I welcome any contribution, furtherance of the analysis of this idea, or criticism of any reasonable kind.
Also, to sidetrack a little bit, may I ask how long it took you to gather these thoughts and post them? I'm trying to get a sense of how far along I am about gaining a holistic understanding of markets and trading.